Model risk for risk measures: An application to the portfolio selection problem with two metaheuristics.

Abstract

The increasing complexity of financial instruments has caused the need for banks and financial institutions to employ very sophisticated models to deal with them. The implementation and use of these model must be done consciously, otherwise Model Risk (MR) may arise. The significant involvement of models in the Great Financial Crisis of 2007 have highlighted the need of introducing a stringent regulatory framework to tackle this problem. Both the US and EU regulators have issued guidelines in order to deal with MR, proposing the so called Model Risk Management framework. However, all these attempts are more focused in providing a qualitative approach to MR, and no compulsory and clearly defined procedure has been drafted to assess MR in a more quantitative way. In this paper, I will analyse the problem of MR for risk measures, considering the Value at Risk (VaR) and the Expected Shortfall (ES), and presenting the most advanced techniques in the literature. Then, I will present a concrete application of these two risk measures, focusing on the portfolio selection problem with the aim of assessing MR deriving form their use. However, because I want a more realistic problem, I will introduce complex constraints that makes the portfolio selection a NP-hard problem, for which no exact method is able to find a solution. Thus, I will introduce two approximated techniques, that fall into metaheuristics algorithms’ family. More in detail, I will apply the Particle Swarm Optimization (PSO) and the Grey Wolf Optimization (GWO). Here, another component of MR deriving from the use of these two models will rise. Thus, after having discussed these two techniques and their application to the portfolio selection problem, I will apply them to eleven securities taken from the S&P 500 index in order to define the optimal portfolio. I will consider two cases for each metaheuristics: one with each of the two risk measures. Thus, I will have four models to analyse: I will assess MR of VaR when applied to the PSO and I will compare it when applied to the GWO. Then I will repeat the same procedure for ES. In this way, I will compare the results analysing both the MR deriving form the choice of the risk measure and from the choice of the metaheuristic. In this manner I will be able to perform a transversal analysis including both the qualitative and the quantitative aspects of MR.